
MINISTRY OF EDUCATION
AND TRAINING
VIETNAM ACADEMY OF SCIENCE
AND TECHNOLOGY
GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY
……..….***…………
NGUYEN THI KIM NGAN
SIMPLE 3-3-1 MODEL AND 3-2-2-1 MODEL FOR DARK
MATTER AND NEUTRINO MASSES
Speciality: Theoretical and mathematical physics
Code: 62 44 01 03
SUMMARY OF THE PHD THESIS
Hanoi – 2018

This thesis was completed at Graduate University of Science and
Technology, Vietnam Academy of Science and Technology.
Supervisors: Dr. Phung Van Dong
Prof. Hoang Ngoc Long
Referee 1: Prof. Dang Van Soa
Referee 2: Dr. Dinh Nguyen Dinh
Referee 3: Dr. Tran Minh Hieu
This dissertation will be defended in front of the evaluating assembly at
academy level, place of defending: meeting room, Graduate University
of Science and Technology, Vietnam Academy of Science and
Technology.
This thesis can be studied at:
- The Library of Graduate University of Science and Technology
- The Vietnam National Library

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INTRODUCTION
The Standard Model (SM) has been successful in exactly pre-
dicting many observational experimental results. Successes of SM
can be mentioned such as predicting the Z and W boson, gluons,
c (charm) quark, t (top) quark and b (bottom) quark before they
were observed by the experiments. One of those is prediction of
Higgs boson recently discovered by LHC (Large Hadron Collider)
at CERN with the 125 GeV mass. This is the last particle predicted
by SM.
However, to this day there are much experimental data re-
maining beyond prediction of SM, such as:
•Why does t (top) quark have the uncommon heavy mass? SM
predicted t quark has the approximate 10 GeV mass while the
experimental result of Tevatron at Fermilab in 1995 demon-
strated that t quark has the 173 GeV mass.
•The early universe is a quantum system, therefore the number
of particles equals to the one of anti-particles, why the present
universe only includes matter constituted by particles, there
is no evidence for the existence of antimatter structured by
anti-particles, called matter-antimatter asymmetry or baryon
asymmetry.
•SM predicted neutrinos have zero masses because they do
not have the right-handed components and lepton number is
conserved. However, the solar, atmospheric, accelerator and
reactor neutrino experiments have predicated in most of 20
years that there are neutrino ocillations when they propa-
gate a long enough journey. This requires neutrinos to have
nonzero masses (even if they are smaller than 1 eV) and mix-
ing. There are three flavours of neutrinos and their mixing
parameterise through the three Euler angles and three CP vi-
olation phases (1 Dirac phase and 2 Majorana phases). The

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existing data of the recent experiments have showed that the
squared mass differences and the mixing angles of neutrinos
have their defined values. There is large mixing between the
electron neutrino and the muon neutrino, between the muon
neutrino and the tau neutrino, while there is small mixing
(different to zero) between the electron neutrino and the tau
neutrino. This is completely different from the quark mixing
(all of them are small). The neutrino experiments can just
determine the Dirac phase which can be different to zero and
can not define the Majorana phases. Then, are the neutrinos
Dirac or Majorana fermions? How can generate the naturally
small neutrino masses which are appropriate for the exper-
imental data? why does the flavour mixing of quarks and
leptons have the completely determined mixing angles? If
there is the existence of right-handed neutrinos νaR they are
colorless, null isospin and null weak hypercharge. Thus, they
do not have gauge interactions, called sterile particles. How-
ever, they can be meaningful in generating neutrino masses
and in the baryon number asymmetry of the universe. In fact,
when νaR is added neutrinos can get Dirac masses because of
the interaction with the Higgs boson, mD∼v(electroweak
scale), which is similar to the charged fermions. Because νaR
is the singlet of SM they can get large Majorana masses, mR,
which violate lepton number. As a result, the active neutri-
nos ∼νaL gain Majorana masses by the seesaw mechanism,
mL=−(mD)2/mR, which is naturally small because of the
condition mR≫mD. It is similar to The Grand Unified The-
ory (GUT) SO(10) that the Dirac masses are proportional to
the electroweak scale, mD∼100 GeV. The active neutrinos
mL∼eV , then mR∼1013 GeV is in the GUT scale and
this is a motivation of the GUT, SO(10). However, the GUT
is difficult to observe by the experiments and encounters the
problem of unnatural hierarchy. The idea of the GUT can be
rejected and mRis imposed so that mR∼TeV, this scale is
discovered by LHC, then the value of mDis approximately
the electron mass. We have the seesaw mechanism at TeV
scale. Yet, a new problem arises is that what is the nature of
right-handed neutrinos (νaR)?
•One of the problems has recently attracted to the theoreti-
cal and experimental physicists is that the existence of the

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amount of unobserved matter (Dark Matter - DM). This day,
there are two viewpoints about DM. Those are the baryonic
DM and non-baryonic DM. The candidates of baryonic DM
are neutron stars or black holes which is a research field of
astrophysics and cosmology, while the ones of non-baryonic
DM are WIMPs (Weakly Interacting Massive Particles) which
are massive particles, and interact very weakly with normal
particles. WIMPs are the objects searched by the elementary
particle physicists. From the point of view of particle physics,
a DM particle must be an electrically neutral particle, stable
and satisfy the relic density of DM. Although WIMPs have
been still found at the colliders, a variety of evidence from as-
trophysics and cosmology has confirmed the existence of DM
in the recent decades. The typical astrophysical evidence in
recent data from the Planck’s satellite shows that the amount
of non-baryonic DM in the universe accounts for 26.8%, which
is different to 23% of the previous WMAP data. In fact, SM
is proven to contain any particle that is a candidate for DM.
•An another current noticeable problem for theoretical physi-
cists is the experimental signal obtained in 2014 at LHCb on
B meson anomaly decays with 3.5 σin comparison to the
SM prediction. This shows there is the violation of the lep-
ton flavour universality or in other words there is the lepton
flavour non-universality (LNU) that is different to the lepton
flavour universality in SM.
For these reasons, we find that SM is not a complete theory
for particle physics, so SM need to be expanded. Now, a physical
model must satisfy the following requirements: i) At low energy
(about 200 GeV), the model must include SM. ii) The neutrino
masses and mixing angles consistent with the neutrino oscillation
experiments. iii) Explain the baryon asymmetry of the Universe
(BAU). iv) Higgs spectrum consistent with current data Higgs,
contain the SM Higgs-like particle which has characteristics similar
to the Higgs of SM. v) Contain the new particles which are the
candidates for DM. However, new physical models are built initially
so that they satisfy the certain aforementioned requirements and
some experimental results which recently discovered. These models
will continue to be completed progressively to fully explain the
existing experimental results. In the current expanded SM models,
the experimental data on neutrino oscillations and DM are the